'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Which means for our asset as example:- Compared with the benchmark SPY (120.8%) in the period of the last 5 years, the total return, or performance of 1165.4% of ProShares UltraPro QQQ is greater, thus better.
- Looking at total return, or increase in value in of 362.2% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (66.3%).

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Which means for our asset as example:- Looking at the annual performance (CAGR) of 66.2% in the last 5 years of ProShares UltraPro QQQ, we see it is relatively greater, thus better in comparison to the benchmark SPY (17.2%)
- Looking at annual return (CAGR) in of 66.5% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (18.5%).

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Applying this definition to our asset in some examples:- The 30 days standard deviation over 5 years of ProShares UltraPro QQQ is 65.1%, which is higher, thus worse compared to the benchmark SPY (18.7%) in the same period.
- During the last 3 years, the 30 days standard deviation is 76.8%, which is larger, thus worse than the value of 22.4% from the benchmark.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Which means for our asset as example:- The downside deviation over 5 years of ProShares UltraPro QQQ is 46.7%, which is larger, thus worse compared to the benchmark SPY (13.6%) in the same period.
- Compared with SPY (16.3%) in the period of the last 3 years, the downside risk of 55.1% is higher, thus worse.

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.78) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.98 of ProShares UltraPro QQQ is greater, thus better.
- Compared with SPY (0.71) in the period of the last 3 years, the Sharpe Ratio of 0.83 is greater, thus better.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Applying this definition to our asset in some examples:- The ratio of annual return and downside deviation over 5 years of ProShares UltraPro QQQ is 1.36, which is larger, thus better compared to the benchmark SPY (1.08) in the same period.
- Looking at downside risk / excess return profile in of 1.16 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (0.98).

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Applying this definition to our asset in some examples:- The Ulcer Index over 5 years of ProShares UltraPro QQQ is 18 , which is larger, thus worse compared to the benchmark SPY (5.59 ) in the same period.
- During the last 3 years, the Ulcer Ratio is 23 , which is larger, thus worse than the value of 6.83 from the benchmark.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Which means for our asset as example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum drop from peak to valley of -69.9 days of ProShares UltraPro QQQ is smaller, thus worse.
- During the last 3 years, the maximum drop from peak to valley is -69.9 days, which is lower, thus worse than the value of -33.7 days from the benchmark.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Which means for our asset as example:- The maximum days below previous high over 5 years of ProShares UltraPro QQQ is 296 days, which is higher, thus worse compared to the benchmark SPY (139 days) in the same period.
- Looking at maximum days under water in of 296 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (139 days).

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Applying this definition to our asset in some examples:- The average days below previous high over 5 years of ProShares UltraPro QQQ is 56 days, which is larger, thus worse compared to the benchmark SPY (33 days) in the same period.
- Compared with SPY (35 days) in the period of the last 3 years, the average time in days below previous high water mark of 80 days is greater, thus worse.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares UltraPro QQQ are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.